Linear methods in the study of automorphisms

Motivation: Studying automorphisms and their fixed points is one of the main areas of research in Group Theory. For soluble and nilpotent groups, it is natural to use the advantages of linear methods of representation theory and Lie ring theory. For finite groups in particular, in view of the classification of finite simple groups, many questions are now largely reduced to soluble and nilpotent groups. List of topics: 1. Automorphisms as linear transformations. 2. Clifford and Hall--Higman--type theorems. 3. Bounding Fitting height. 4. Powerful $p$-groups. 5. Lie ring methods. 6. Using EXP and LOG functors. 7. Method of generalized centralizers. 8. Elimination of operators by nilpotenc